TSTP Solution File: ITP012^3 by Leo-III---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : ITP012^3 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  7 07:46:46 EDT 2024

% Result   : Theorem 3.23s 1.71s
% Output   : Refutation 3.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   16 (   3 unt;   6 typ;   0 def)
%            Number of atoms       :   35 (  11 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :   79 (   2   ~;   0   |;   2   &;  70   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   23 (   0   ^  23   !;   0   ?;  23   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tyop_2Einteger_2Eint_type,type,
    tyop_2Einteger_2Eint: $tType ).

thf(tyop_2Emin_2Ebool_type,type,
    tyop_2Emin_2Ebool: $tType ).

thf(c_2Einteger_2Eint__add_type,type,
    c_2Einteger_2Eint__add: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__divides_type,type,
    c_2Einteger_2Eint__divides: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).

thf(c_2Einteger_2Eint__neg_type,type,
    c_2Einteger_2Eint__neg: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__sub_type,type,
    c_2Einteger_2Eint__sub: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(1,conjecture,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__sub @ C @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RSUB) ).

thf(2,negated_conjecture,
    ~ ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__divides @ A @ B )
       => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__sub @ C @ B ) )
          = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__divides @ A @ B )
       => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__sub @ C @ B ) )
          = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ B )
      = ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2Eint__sub) ).

thf(11,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ B )
      = ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ C @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RADD) ).

thf(14,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ C @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ B ) )
      & ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__neg @ A ) @ B )
        = ( c_2Einteger_2Eint__divides @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__NEG) ).

thf(18,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ B ) )
      & ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__neg @ A ) @ B )
        = ( c_2Einteger_2Eint__divides @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(32,plain,
    $false,
    inference(e,[status(thm)],[6,11,14,18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP012^3 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n006.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May  6 14:49:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.97/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.35/1.00  % [INFO] 	 Parsing done (142ms). 
% 1.35/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.22  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.28  % [INFO] 	 Found a conjecture and 32 axioms. Running axiom selection ... 
% 2.00/1.31  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 29 axioms). 
% 2.00/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.00/1.32  % [INFO] 	 Type checking passed. 
% 2.00/1.32  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 3.23/1.71  % External prover 'e' found a proof!
% 3.23/1.71  % [INFO] 	 Killing All external provers ... 
% 3.23/1.71  % Time passed: 1178ms (effective reasoning time: 695ms)
% 3.23/1.71  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.23/1.71  % Axioms used in derivation (3): thm_2Einteger_2Eint__sub, thm_2Einteger_2EINT__DIVIDES__RADD, thm_2Einteger_2EINT__DIVIDES__NEG
% 3.23/1.71  % No. of inferences in proof: 10
% 3.23/1.71  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1178 ms resp. 695 ms w/o parsing
% 3.23/1.73  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.23/1.73  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------